Stair Calculator

If the run of each step is 10 inches and there are 12 steps, calculate the total run of the staircase.

Solution: The total run is: \( \text{Total Run} = \text{Run per Step} \times \text{Number of Steps} \)
Substituting values: \( \text{Total Run} = 10 \, \text{inches} \times 12 = 120 \, \text{inches} \)

If the total rise is 84 inches and the total run is 120 inches, calculate the angle of the staircase in degrees.

Solution: The angle is given by: \( \theta = \arctan\left(\frac{\text{Total Rise}}{\text{Total Run}}\right) \)
Substituting values: \( \theta = \arctan\left(\frac{84}{120}\right) \approx 35.07^\circ \)

A staircase has 12 steps, each with a run of 10 inches. Calculate the total staircase run.

Solution: The total run is given by: \( \text{Total Run} = \text{Number of Steps} \times \text{Step Run} \)
Substituting values: \( \text{Total Run} = 12 \times 10 = 120 \, \text{inches} \)

A staircase has 15 steps, each with a rise of 7 inches. Calculate the total staircase height.

Solution: The total height is given by: \( \text{Total Height} = \text{Number of Steps} \times \text{Step Rise} \)
Substituting values: \( \text{Total Height} = 15 \times 7 = 105 \, \text{inches} \)

If the total run is 144 inches and there are 18 steps, calculate the tread depth.

Solution: The tread depth is given by: \( \text{Tread Depth} = \frac{\text{Total Run}}{\text{Number of Steps}} \)
Substituting values: \( \text{Tread Depth} = \frac{144}{18} = 8 \, \text{inches} \)

A step has a rise of 7 inches and a run of 11 inches. Calculate the slope ratio.

Solution: The slope ratio is given by: \( \text{Slope Ratio} = \frac{\text{Step Rise}}{\text{Step Run}} \)
Substituting values: \( \text{Slope Ratio} = \frac{7}{11} \approx 0.636 \)

A staircase needs to cover a total height of 96 inches with steps of 8 inches rise each. How many steps are required?

Solution: The number of steps is given by: \( \text{Number of Steps} = \frac{\text{Total Height}}{\text{Step Rise}} \)
Substituting values: \( \text{Number of Steps} = \frac{96}{8} = 12 \, \text{steps} \)

A step has a rise of 6 inches and a run of 10 inches. Calculate the diagonal length of the step.

Solution: The diagonal is given by: \( \text{Diagonal} = \sqrt{\text{Step Rise}^2 + \text{Step Run}^2} \)
Substituting values: \( \text{Diagonal} = \sqrt{6^2 + 10^2} = \sqrt{36 + 100} = \sqrt{136} \approx 11.66 \, \text{inches} \)